The performance of remote estimation over wireless channels is strongly affected by sensor data losses due to interference. Although the impact of interference can be alleviated by applying cognitive radio technique which features in spectrum sensing and transmitting data only on clear channels, the introduction of spectrum sensing incurs extra energy expenditure. In this paper, we investigate the problem of energy-efficient spectrum sensing for remotely estimating the state of a general linear dynamic system, and formulate an optimization problem which minimizes the total sensor energy consumption while guaranteeing a desired level of estimation performance. We model the problem as a mixed integer nonlinear program and propose a simulated annealing based optimization algorithm which jointly addresses when to perform sensing, which channels to sense, in what order and how long to scan each channel. Simulation results demonstrate that the proposed algorithm well balances the sensing energy and transmission energy expenditure and can achieve the desired estimation performance.



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